Symbolic Disentangled Representations in Hyperdimensional Latent Space

The idea of the disentangled representations is to reduce the data to a set of generative factors which generate it. Usually, such representations are vectors in the latent space, in which each coordinate corresponds to one of the generative factors. Then the object represented in this way can be modified by changing the value of a specific coordinate. But first, we need to determine which coordinate handles the desired generative factor, which can be complex with a high vector dimension. In this paper, we propose to represent each generative factor as a vector of the same dimension as the resulting representation. This is possible by using Hyperdimensional Computing principles (also known as Vector Symbolic Architectures), which represent symbols as high-dimensional vectors. They allow us to operate on symbols using vector operations, which leads to a simple and interpretable modification of the object in the latent space. We show it on the objects from dSprites and CLEVR datasets and provide an extensive analysis of learned symbolic disentangled representations in hyperdimensional latent space.